1. Field of the invention
The present invention relates to a vibrating element capable of vibrating under an expansion mode and, more particularly, to a piezoelectric vibrator defined by a thin piezoelectric film deposited on a substrate made of a constant modulus alloy and a vibration electrode film deposited on the piezoelectric film. It also relates to a method for adjusting the vibration frequency of such a vibrating element.
2. Description of the Prior Art
As shown in FIG. 1, a typical piezoelectric vibrator 101 of the prior art has a substrate 102 on which a piezoelectric film 103 is deposited by way of sputtering, and a vibration electrode film 104 which is further deposited on piezoelectric film 103. The electric signal is applied between substrate 102 and electrode film 104.
In FIG. 2, an equivalent circuit of vibrating element 101 is shown. The equivalent circuit includes a resonance inductance L, a resistance R and a series capacitance Cs, which are connected in series, and a parallel capacitance Cp, which is connected in parallel with the series connection of L, R and Cs. The vibration characteristics can be evaluated by using a ratio .phi.(=Cp/Cs), such that the smaller the ratio .phi., the better the vibration characteristics.
The vibration frequency is determined by width between opposite sides 105a and 105b of the vibrator 101 such that the vibration frequency becomes higher as the width becomes narrower. Accordingly, the vibration frequency has in the past been adjusted by trimming the opposite sides 105a, 105b along the chain lines shown in FIG. 1(a). However, cutting the opposite sides in a plane is very difficult.
For this reason it has been proposed that instead of cutting the opposite sides, slits Sa and Sb be formed at opposite sides 105a and 105b, l as shown in FIG. 1(a). Although this method is easier than cutting the opposite sides, the formation of such slits Sa and Sb results in the increase of the ratio .phi. and, at the same time, in the decrease of the difference DF between the antiresonant frequency and resonant frequency, thus deteriorating the vibration characteristics.